This article reports a Conversation Session presented at ICOCIME 2, discussing actions undertaken by three PhD students of the Post-Graduate Program in Mathematics Teaching (PEMAT), of the Federal University of Rio de Janeiro. Innovative evaluation proposals differ from traditional models, both in terms of the assessment of students’ performance, and in relation to the attitudes of the teachers responsible for the assignment of the grades. Commonly associated with tests, school assessments in mathematics are instruments with generally well-defined characteristics: individual, written, and time bounded. They are usually composed by single response questions and offer generic treatment to all students with the intention of being neutral. Usually applied at the end of a learning cycle, the tests are conceived in a positivist philosophy that attributes to this instrument a character of impartiality and justice. Insubordinate and creative proposals indicate the need to know the students involved in the process, in order to establish a meaningful teaching and learning relationship. In a critical and progressive perspective of the evaluation, it is necessary to consider democracy in the evaluating instrument to build bridges between teachers and students, avoiding the deviations of subjectivity and biases in the correction of the tests.